Complete the Equation: How to Finish Subtraction and Addition Sentences with Mixed Numbers

When presented with incomplete addition or subtraction sentences involving mixed numbers, the challenge lies in determining the missing value. In this guide, we’ll explore how to finish such sentences, ensuring a clear understanding of the operations involved.

Step-by-step Guide to Complete the Equation:

1. Understanding the Sentence Structure: 

Incomplete sentences will typically have a missing value, represented by a blank or a variable (like \(x\)). Your task is to determine this missing value.

2. Approaching Addition Sentences: 

For addition:

– Begin by adding/subtracting the fractional parts. If the fractions have different denominators, find a common denominator.

– Next, add/subtract the whole numbers.

– Combine the results to get the final mixed number.

3. Approaching Subtraction Sentences: 

For subtraction:

– Start by subtracting the fractional parts. If the fraction from which you are subtracting is larger than the first fraction, borrow from the whole number.

– Then, subtract the whole numbers.

– Combine the results to get the final mixed number.

Example 1 (Addition): 

Complete the sentence: \( 2 \frac{1}{4} + 3 \frac{3}{4} = \_\_\_\_ \) 

Solution: 

Adding the fractions: \(\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1\) 

Adding the whole numbers: \(2 + 3 + 1 (from the fractions) = 6\) 

The completed sentence is: \( 2 \frac{1}{4} + 3 \frac{3}{4} = 6 \)

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Example 2 (Subtraction): 

Complete the sentence: \( 5 \frac{3}{5} – 2 \frac{2}{5} = \_\_\_\_ \) 

Solution: 

Subtracting the fractions: \(\frac{3}{5} – \frac{2}{5} = \frac{1}{5}\) 

Subtracting the whole numbers: \(5 – 2 = 3\) 

The completed sentence is: \( 5 \frac{3}{5} – 2 \frac{2}{5} = 3 \frac{1}{5} \)

Practice Questions: 

1. Complete the sentence: \( 4 \frac{2}{7} + 3 \frac{5}{7} = \_\_\_\_ \)

2. Complete the sentence: \( 7 \frac{3}{8} – 5 \frac{1}{8} = \_\_\_\_ \)

3. Complete the sentence: \( 6 \frac{1}{6} + 2 \frac{5}{6} = \_\_\_\_ \)

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Answers: 

1. \( 8 \)

2. \( 2 \frac{2}{8} \) or \( 2 \frac{1}{4} \)

3. \( 9 \)

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